Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). 1 HW 14 HW 14 More on Moderators Calculate the moderating power and ratio for pure D 2 O as well as for D 2 O contaminated with a) 0.25% and b) 1% H 2 O. Comment on the results. In CANDU systems there is a need for heavy water upgradors.
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Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh). 1 HW 14 More on Moderators Calculate the moderating power and ratio for pure D 2 O as well.
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Calculate the moderating power and ratio for pure D2O as well as for D2O contaminated with a) 0.25% and b) 1% H2O.Comment on the results.In CANDU systems there is a need for heavy water upgradors.
ContinuousContinuous slowing down model or Fermi model. slowing down model or Fermi model.
• The scattering of neutrons is isotropic in the CM system, thus is independent on neutron energy. also represents the average increase in lethargy per collision, i.e. after n collisions the neutron lethargy will be increased by n units.
• Materials of low mass number is large Fermi model is inapplicable.
One-Speed Interactions• Particular general.Recall:• Neutrons don’t have a chance to interact with each other (review test!) Simultaneous beams, different intensities, same energy:
Ft = t (IA + IB + IC + …) = t (nA + nB + nC + …)v• In a reactor, if neutrons are moving in all directions n = nA + nB + nC + …
Neutrons per cm3 at r with energy interval (E, E+dE) whose velocity vector lies within d about .
• Generalize to include energy
4
),,(),( dEdErndEErn
0 4
),,()(
dEdErnrn
dEErEdEEvErnEdEErR tt ),()()(),()(),(
0
),()()( dEErErR t
Thus knowing the material properties t and the neutron flux as a function of space and energy, we can calculate the interaction rate throughout the reactor.
Fick’s LawAssumptions:1.The medium is infinite.2.The medium is uniform 3.There are no neutron sources in the medium.4.Scattering is isotropic in the lab. coordinate system.5.The neutron flux is a slowly varying function of position.6.The neutron flux is not a function of time.
• Diffusion: random walk of an ensemble of particles from region of high “concentration” to region of small “concentration”.• Flow is proportional to the negative gradient of the “concentration”.